For your consideration; Dan’s reading notes on Krantz’s How to Teach Mathematics (PDF):

Krantz-Notes-Public

Discussing:

• Steven G. Krantz, How to Teach Mathematics, Chapters 4-6

Attending:

• Daniel, Kristin, Tian

Points:

• Students being surprised at learning any new skill in a college math class (after many years of algebra review). Complaints/grievances.
• Students being accustomed to scaling/extra credit to make sure they pass (instead of rigorous standards & hard work). History of K-12, etc.
• Major CUNY changes to placement, remediation, low-level courses, and high-level prerequisite accounting (i.e., eliminate high-level courses in STEM majors?).
• Likely very few M2 courses in future (only for STEM students who do not pass elementary algebra placement). New non-algebra course for non-STEM majors (majority of clientele). For M2, CUNY uniform final exam will not require passing grade (same for English writing test).
• Begs question: Will placement tests still be given? Will uniform final still be given, or eliminated?
• Biology department offers 1-2 credit math supplements linked to sections of non-major biology (e.g., BIO 33). Custom workbook.
• Students pt-in, scattered through other sections.
• Majors are given a 4-day workshop in math before the semester begins (grant-funded; supplies food, mentors, core textbook at end).
• Pre- and post-surveys.
• Referring students with prerequisite deficiencies to consultations in office hours, and/or the math workshop.
• Are all freshmen now in learning communities?
• Can we get a supplement section to prerequisite skills for math courses?

Discussing:

• Steven G. Krantz, How to Teach Mathematics, Chapters 3-4

Attending:

• Daniel, Patrick, Kristen, Aleksandr, Deborah, Eva, Tian (and Sara K.)

Points:

• What else can this group do to move forward with better math teaching at KCC?
• STEM Vision Committee — team up with them
• Run a pilot somehow using new strategies to teach math, and then follow students to see how they do in chemistry, biology, etc.
• With the doing away of math requirements (algebra) for non-STEM majors, we are separating STEM and non-STEM tracks early and with little chance for switching tracks later in education or career without starting over from square one.
• Elementary Algebra M2 is now a multiple-choice test, with a calculator, and students do not have to pass the test to pass the class. As of next semester, students do not need to even pass this class to graduate.
• Given all of these things we can’t control, is there anything we can do? Would expanding the Math Workshop help? It would help some students, but probably not a majority.
• Some research claims remediation never solves the problem — ongoing support will always be needed.
• What other things can we do? Give more practice — students do know some math, but need practice & feedback.
• Physical sciences uses ALEKS (others: MathXL, WebWork.)
• One observation: Even with ALEKS homework 25% of grade, some students still don’t do it. Others find online homework helpful.
• Another strategy is to spend some time on definitions, so that the words in word problems are understood.
• Ask students to draw what the instructions say (show them an example; in chemistry, physics, biology).
• CHE 12 “all about logs”, but only prerequisite is MAT 9; logs covered briefly in MAT 14.
• Many students are trained to be passive learners, so much so that many consider preparing for class & doing the exercises ahead of time on their own as cheating.
• How has this FIG affected your teaching practice? For most, understanding what math is needed for science courses, vs. what math is taught in prerequisites, has been revelatory and helpful.

Discussing:

• Steven G. Krantz, How to Teach Mathematics, Chapters 1-3

Attending:

• Aleksandr Gorbenko, Patrick Lloyd, Daniel Collins, Kristin Polizotto, Tian Cai, Deborah Berhanu

Points:

• Question: What did you agree or disagree with?
• Moore Method: Surely inappropriate for our students.
• Question: Why are KCC students unprepared?
• K-12 prep as a problem for KCC students.
• Math anxiety among K-6 teachers, esp. females, who then communicate this to students (esp. girls who identify with teacher).
• The students get high school diploma without really learning math.
• Comparison to teacher qualifications in different countries/states.
• Specialist K-6 teachers would be the #1 thing to change (DRC).
• Working in groups outside of class — effective but possibly a challenge for our students — culturally, time constraints, socially, etc.
• Groups only effective if carefully chosen — someone who knows what they’re doing.
• Asian students may know how to do the problems & get good grades, but necessarily able to apply or engage with the world with that knowledge.
• Influence of home environment (in terms of academic discipline) and of social class.
• Do the suggestions in this book help all students? Effective across the board? (Probably.)
• Students cannot set up a problem — logically — because that unit is skipped in K-12.
• Logic not required at KCC (even in math department) — inductive & deductive reasoning is not required.
• Krantz recommends examples, then building/developing theorem.
• Other option: Principle/theorem, then proof, then examples (traditional in definition-theorem-proof-application).
• Daniel thinks traditional is better for students who will not be mathematicians. But Tian/Pat thought examples earlier on was better.
• Next meeting: Nov-22nd at 12:40 PM (to include outside grant observer).

Discussing:

• Steven G. Krantz, How to Teach Mathematics, Preface

Attending:

• Daniel Collins, Emral Devany

Points:

(1) Prerequisite Challenges

• Started with an overview of the book, as some people were just being informed/picking it up today. In future sessions we’ll plan to cover the main chapters, and try to find ways to attract more attendees.
• Discussed challenges in classes where many students don’t have the expected prerequisite math skills. (For example: Integrated Seminar in Biology, including majors and practicing nurses).
• Examples: Estimated 1/3 may not be able to compute a percent increase between two numbers (or its inverse). This would be used in a metabolism problem, etc. Note that this was previously tested on the CUNY-wide remedial CEAFE (CUNY Elematary Algebra Final Exam), but was recently removed as it was considered too difficult.
• Unfamiliarity with efficient conversion methods: Biology, using the metric units (multiplying by 1000 vs. moving point 3 places). Statistics, converting percent to decimal (dividing by 100 vs moving point 2 places).
• Problems with students knowing algebra but not arithmetic. (CUNY entry testing with COMPASS aborted testing on arithmetic if algebra was passed; this may be reversed with new Accu-Placer test, which combines both in a single test/score).
• Students passing math via raw, herculean memorization of procedures (much harder). Understanding concepts can make these methods trivial to remember.
• Problem of instructor not realizing basic things that students don’t know, possibly for many semesters or years (e.g., types of energy, conversions, checking solutions to equations).
• History of repeating definitions without quantitative applications in some prior science classes.

(2) Testing and Time

• Test-taking history, where students are mostly exposed to multiple-choice tests and tricks to pass them (Krantz in Ch. 2 strongly recommends non-multiple-choice tests for this reason).
• Need to test/quiz on exactly the basic skills practiced in class (not more exotic extensions).
• But: Time constraints on grading, plus assignments, may bias towards multiple-choice tests.
• Suggest: Tests that are part multiple-choice, part short answer (possibly fewer in larger classes).
• Suggestion: Using a point-and-click Rubric in Blackboard for quickly grading assignments and providing feedback (e.g. in a programming course).
• Krantz in Ch. 1: Time management in class: How to avoid an activity that goes long, cut off in middle by end of session, need to pick up in middle next time?
• Prepare 2-3 short exercises in class so one or more can be cut for time if needed.
• Permitting students to go early if they complete exercise quickly: Can give extra attention for other students (with reduced anxiety over struggles in front of peers).

(3) K-3 Experience

• Current student experience in K-6: 1st grade — Test correct performance on several defined procedures. 2nd grade — Give credit for any generation of correct answer, no matter how. Instruction on “how to take multiple-choice test” tricks. 3rd grade — Standardized multiple-choice tests begin, used to assess schools. Seemingly large strategic shift at the point when school needs high grades on standardized tests.
• Common Core complaints: Often unjustified.
• College students not knowing 2nd-3rd grade concepts (scientific method, etc.)
• Passing all students K-12 (no hold backs).

Fall 2016 Book: Stephen G. Krantz, How to Teach Mathematics (3^rd Ed.), published by the AMS (American Mathematical Society), 2015. This an update from earlier editions published in 1993 and 1999.

Book Availability: KCTL has a supply of books for our fall reading. If you can commit to joining at least two of our fall discussion meetings, then you can pick up a book for free in M-391.

Discussion Meetings: Mondays, 11:30 AM – 12:30 PM, in M-391 on the following dates.

• Sep-26: Ch. 1-2, “Guiding principles”, “Practical matters”.
• Oct-24: Ch. 3-4, “Spiritual matters”, “The electronic world”.
• Nov-21: Ch. 5-6, “Difficult matters”, “A new beginning”.

More Optional Readings: Available online.

• End matter (contents, preface, bibliography, index): www.ams.org/books/mbk/089/mbk089-endmatter.pdf
• Appendix from earlier edition (critical responses): www.math.wustl.edu/~sk/teachapps.pdf